Problem: Takahashi loves sorting.

He has a permutation (p_1,p_2,...,p_N) of the integers from 1 through N. Now, he will repeat the following operation until the permutation becomes (1,2,...,N):

* First, we will define high and low elements in the permutation, as follows. The i-th element in the permutation is high if the maximum element between the 1-st and i-th elements, inclusive, is the i-th element itself, and otherwise the i-th element is low.
* Then, let a_1,a_2,...,a_k be the values of the high elements, and b_1,b_2,...,b_{N-k} be the values of the low elements in the current permutation, in the order they appear in it.
* Lastly, rearrange the permutation into (b_1,b_2,...,b_{N-k},a_1,a_2,...,a_k).



How many operations are necessary until the permutation is sorted?

Constraints

* 1 ≤ N ≤ 2×10^5
* (p_1,p_2,...,p_N) is a permutation of the integers from 1 through N.

Input

Input is given from Standard Input in the following format:


N
p_1 p_2 ... p_N


Output

Print the number of operations that are necessary until the permutation is sorted.

Examples

Input

5
3 5 1 2 4


Output

3


Input

5
5 4 3 2 1


Output

4


Input

10
2 10 5 7 3 6 4 9 8 1


Output

6

Solution (in CPP):

Solution:
#include<iostream>
#include<cstdio>
#include<cstring>
#define N 200010
using namespace std;
int p[N];
int main()
{
	int n;
	scanf("%d",&n);
	for(int i=1;i<=n;i++)
	{
		int a;
		scanf("%d",&a);
		p[a]=i;
	}
	int u=n-1;
	while(u && p[u]<p[u+1]) u--;
	if(!u){puts("0");return 0;}
	int ans=1,pre=u+1;
	for(;u;u--)
	{
		if(p[pre]<=p[u] && p[u]<=p[u+1]) continue;
		if(p[u]<=p[u+1] && p[u+1]<=p[pre]) continue;
		if(p[u+1]<=p[pre] && p[pre]<=p[u]) continue;
		ans++;
		pre=u+1;
	}
	printf("%d",ans);
	return 0;
}